FFT和IFFT的C代码实现

#include <stdio.h>
#include <stdlib.h>
#include <math.h>


#define intsize sizeof(int)
#define complexsize sizeof(complex)
#define PI 3.1415926


int *a,*b;
int nLen,init_nLen,mLen,init_mLen,N,M;
FILE *dataFile;


typedef struct{
float real;
float image;
}complex;


complex *A,*A_In,*W;


complex Add(complex, complex);
complex Sub(complex, complex);
complex Mul(complex, complex);
int calculate_M(int);
void reverse(int,int);
void readData();
void fft(int,int);
void Ifft();
void printResult_fft();
void printResult_Ifft();


int main()
{
int i,j;
readData();
A = (complex *)malloc(complexsize*nLen);
reverse(nLen,N);
for(i=0; i<mLen; i++)
{
for(j=0; j<nLen; j++)
{
A[j].real = A_In[i*nLen+b[j]].real;
A[j].image = A_In[i*nLen+b[j]].image;
}


fft(nLen,N);
for(j=0; j<nLen; j++)
{
A_In[i*nLen+j].real = A[j].real;
A_In[i*nLen+j].image = A[j].image;
}
}


free(a);
free(b);
free(A);


A = (complex *)malloc(complexsize*mLen);
reverse(mLen,M);
for(i=0; i<nLen; i++)
{
for(j=0; j<mLen; j++)
{
A[j].real = A_In[b[j]*nLen+i].real;
A[j].image = A_In[b[j]*nLen+i].image;
}


fft(mLen,M);
for(j=0; j<mLen; j++)
{
A_In[j*nLen+i].real = A[j].real;
A_In[j*nLen+i].image = A[j].image;
}
}
free(A);
printResult_fft();
Ifft();
printResult_Ifft();
return 0;
}


void readData()
{
int i,j;


dataFile = fopen("dataIn.txt","r");
fscanf(dataFile,"%d %d",&init_mLen,&init_nLen);
M = calculate_M(init_mLen);
N = calculate_M(init_nLen);
nLen = (int)pow(2.0,N);
mLen = (int)pow(2.0,M);
A_In = (complex *)malloc(complexsize*nLen*mLen);


for(i=0; i<init_mLen; i++)
{
for(j=0; j<init_nLen; j++)
{
fscanf(dataFile,"%f",&A_In[i*nLen+j].real);
A_In[i*nLen+j].image = 0.0;
}
}
fclose(dataFile);


for(i=0; i<mLen; i++)
{
for(j=init_nLen; j<nLen; j++)
{
A_In[i*nLen+j].real = 0.0;
A_In[i*nLen+j].image = 0.0;
}
}


for(i=init_mLen; i<mLen; i++)
{
for(j=0; j<init_nLen; j++)
{
A_In[i*nLen+j].real = 0.0;
A_In[i*nLen+j].image = 0.0;
}
}


printf("Reading initial datas:\n");
for(i=0; i<init_mLen; i++)
{
for(j=0; j<init_nLen; j++)
{
if(A_In[i*nLen+j].image < 0)
{ 
printf("%f%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
else
{
printf("%f+%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
}
printf("\n");
}


printf("\n");


printf("Reading formal datas:\n");
for(i=0; i<mLen; i++)
{
for(j=0; j<nLen; j++)
{
if(A_In[i*nLen+j].image < 0)
{ 
printf("%f%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
else
{
printf("%f+%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
}
printf("\n");
}
}




void fft(int fft_nLen, int fft_M)
{
int i;
int lev,dist,p,t;
complex B;


W = (complex *)malloc(complexsize*fft_nLen/2);


for(lev=1; lev<=fft_M; lev++)
{
dist = (int)pow(2.0,lev-1);
for(t=0; t<dist; t++)
{
p = t*(int)pow(2.0,fft_M-lev);
W[p].real = (float)cos(2*PI*p/fft_nLen);
W[p].image = (float)(-1*sin(2*PI*p/fft_nLen));
for(i=t; i<fft_nLen; i=i+(int)pow(2.0,lev))
{
B = Add(A[i],Mul(A[i+dist],W[p]));
A[i+dist] = Sub(A[i],Mul(A[i+dist],W[p]));
A[i].real = B.real;
A[i].image = B.image;
}
}
}


free(W);
}




void printResult_fft()
{
int i,j;


printf("Output FFT results:\n");
for(i=0; i<mLen; i++)
{
for(j=0; j<nLen; j++)
{
if(A_In[i*nLen+j].image < 0)
{
printf("%f%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
else
{
printf("%f+%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
}
printf("\n");
}
}


void printResult_Ifft()
{
int i,j;


printf("Output IFFT results:\n");
for(i=0; i<mLen; i++)
{
for(j=0; j<nLen; j++)
{
if(A_In[i*nLen+j].image < 0)
{
printf("%f%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
else
{
printf("%f+%fi\t",A_In[i*nLen+j].real,A_In[i*nLen+j].image);
}
}
printf("\n");
}


free(A_In);
}


int calculate_M(int len)
{
int i;
int k;


i = 0;
k = 1;
while(k < len)
{
k = k*2;
i++;
}


return i;
}


void reverse(int len, int M)
{
int i,j;


a = (int *)malloc(intsize*M);
b = (int *)malloc(intsize*len);


for(i=0; i<M; i++)
{
a[i] = 0;
}


b[0] = 0;
for(i=1; i<len; i++)
{
j = 0;
while(a[j] != 0)
{
a[j] = 0;
j++;
}


a[j] = 1;
b[i] = 0;
for(j=0; j<M; j++)
{
b[i] = b[i]+a[j]*(int)pow(2.0,M-1-j);
}
}
}


complex Add(complex c1, complex c2)
{
complex c;
c.real = c1.real+c2.real;
c.image = c1.image+c2.image;
return c;
}


complex Sub(complex c1, complex c2)
{
complex c;
c.real = c1.real-c2.real;
c.image = c1.image-c2.image;
return c;
}


complex Mul(complex c1, complex c2)
{
complex c;
c.real = c1.real*c2.real-c1.image*c2.image;
c.image = c1.real*c2.image+c2.real*c1.image;
return c;
}


void Ifft()
{
int i,j;


for(i=0; i<mLen; i++)
{
for(j=0; j<nLen; j++)
{
A_In[i*nLen+j].image = -A_In[i*nLen+j].image;
}
}


A = (complex *)malloc(complexsize*nLen);
reverse(nLen,N);
for(i=0; i<mLen; i++)
{
for(j=0; j<nLen; j++)
{
A[j].real = A_In[i*nLen+b[j]].real;
A[j].image = A_In[i*nLen+b[j]].image;  
}


fft(nLen,N);
for(j=0; j<nLen; j++)
{   
A_In[i*nLen+j].real = A[j].real/nLen;
A_In[i*nLen+j].image = A[j].image/nLen;
}
}
free(A);
free(a);
free(b);


A = (complex *)malloc(complexsize*mLen);
reverse(mLen,M);
for(i=0; i<nLen; i++)
{
for(j=0; j<mLen; j++)
{
A[j].real = A_In[b[j]*nLen+i].real;
A[j].image = A_In[b[j]*nLen+i].image;
}


fft(mLen,M);
for(j=0; j<mLen; j++)
{
A_In[j*nLen+i].real = A[j].real/mLen;
A_In[j*nLen+i].image = A[j].image/mLen;
}
}
free(A);
free(a);
free(b);
}